Question

select the correct answer
this table defines a function

x	7	10	13	16
y	21	30	39	48

which table represents the inverse of the function defined above?
a. | x | 7 | 10 | 13 | 16 |

y

-21

-30

-39

-48

b. | x | -21 | -30 | -39 | -48 |

y

7

10

13

16

c. | x | 21 | 30 | 39 | 48 |

y

7

10

13

16

d. | x | -7 | -10 | -13 | -16 |

y

21

30

39

48

Explanation:

Step1: Recall inverse function definition

To find the inverse of a function defined by a table, we swap the \( x \)-values and \( y \)-values. The original function has pairs \((7, 21)\), \((10, 30)\), \((13, 39)\), \((16, 48)\).

Step2: Swap x and y values

Swapping these pairs gives \((21, 7)\), \((30, 10)\), \((39, 13)\), \((48, 16)\). Now we check the options:

• Option A: Keeps original \( x \)-values, changes \( y \)-signs. Not inverse.
• Option B: Uses negative \( x \)-values (not original \( y \)-values). Incorrect.
• Option C: Has \( x \)-values as original \( y \)-values and \( y \)-values as original \( x \)-values. Matches the swapped pairs.
• Option D: Negates \( x \)-values, keeps original \( y \)-values. Not inverse.

Answer:

C.

x	21	30	39	48